Theory of differential offset continuation

I introduce a partial differential equation to describe the process of prestack reflection data transformation in the offset, midpoint, and time coordinates. The equation is proved theoretically to provide correct kinematics and amplitudes on the transformed constant-offset sections. Solving an initial-value problem with the proposed equation leads to integral and frequency-domain offset continuation operators, which reduce to the known forms of dip moveout operators in the case of continuation to zero offset.